Mr. Pokémon apparently went to the Pokémon Day Care Center, where he first found the Pokémon egg. However, when he returned to the lab, he decided to send it to another professional of Pokémon research to preserve this discovery. This is seen in gameplay of Pokémon Gold, Silver, Crystal and its remakes.

Trivia

He is alerted in the game when your rival steals one of Elm's Starter Pokémon.